Question

An 18000 kg freight car rests against a spring bumper at the end of a railroad track. The spring has constant k=3.2×10^5 N/m. The car is hit by a second car of 9400 kg mass moving at 8.0 m/s , and the two couple together.

Find the maximum compression of the spring.

Find the speed of the two cars when they rebound together from the spring.

Answer 1

here,

mass of freight car , m1 = 18000 kg

mass of second car , m2 = 9400 kg

initial speed of second car , u2 = 8 m/s

let the final speed after the collison be v

using conservation of momentum

m2 * u2 = (m1 + m2) * v

9400 * 8 = ( 9400 + 18000) * v

solving for v

v = 2.74 m/s

spring constant , K = 3.2 * 10^5 N/m

let the maximum compression of the spring be x

using conservation of energy

0.5 * K * x^2 = 0.5 * ( m1 + m2) * v^2

3.2 * 10^5 * x^2 = (18000 + 9400) * 2.74^2

solving for x

x = 0.8 m

the maximum compression of the spring is 0.8 m

the speed of the two cars when they rebound together from the spring is 2.74 m/s